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Incompressible limit of a fluid-particle interaction model. (English) Zbl 07332690
Summary: The incompressible limit of the weak solutions to a fluid-particle interaction model is studied in this paper. By using the relative entropy method and refined energy analysis, we show that, for well-prepared initial data, the weak solutions of the compressible fluid-particle interaction model converge to the strong solution of the incompressible Navier-Stokes equations as long as the Mach number goes to zero. Furthermore, the desired convergence rates are also obtained.
MSC:
35B25 Singular perturbations in context of PDEs
35G25 Initial value problems for nonlinear higher-order PDEs
35Q35 PDEs in connection with fluid mechanics
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